Initialization

Needs["MaTeX`"]
SetOptions[MaTeX,"Preamble"->{"\\usepackage{amssymb,amsmath,latexsym,amsfonts,amsthm,mathpazo,xcolor,bm,mhchem,inputenc,fontenc,txfonts}"}];

HaToeV=27.21138602;

SetDirectory["~/Dropbox/Manuscripts/Ec/data_AS"];

Hilbert spaces

Five-membered ring

(* cyclopentadiene, furan, imidazole, pyrrole, and thiophene *)

{((Binomial[100-5,18-5])^2),((Binomial[90-5,18-5])^2),((Binomial[90-5,18-5])^2),((Binomial[95-5,18-5])^2),((Binomial[94-9,22-9])^2)}//N

Six-membered ring

(* benzene, pyrazine, pyridazine, pyridine, pyrimidine, tetrazine, and triazine *)

{((Binomial[114-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[109-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[94-6,21-6])^2),((Binomial[99-6,21-6])^2)}//N

Molecules

TableForm[{
{MoleculePlot3D[Molecule["cyclopentadiene"]],MoleculePlot3D[Molecule["furan"]],MoleculePlot3D[Molecule["imidazole"]],MoleculePlot3D[Molecule["pyrrole"]],MoleculePlot3D[Molecule["thiophene"]]}
,{"cyclopentadiene","furan","imidazole","pyrrole","thiophene"}
},TableAlignments->Center]
TableForm[{
{MoleculePlot3D[Molecule["benzene"]],MoleculePlot3D[Molecule["pyrazine"]],MoleculePlot3D[Molecule["pyridazine"]],MoleculePlot3D[Molecule["pyridine"]],MoleculePlot3D[Molecule["pyrimidine"]],MoleculePlot3D[Molecule["1,2,4,5-tetrazine"]],MoleculePlot3D[Molecule["1,3,5-triazine"]]}
,{"benzene","pyrazine","pyridazine","pyridine","pyrimidine","s-tetrazine","s-triazine"}
},TableAlignments->Center]

Modules

(Subscript[E, var]) vs (Subscript[N, det])

EvsNdet[Mol_,Range_,ExpFig_]:=Module[
{NO,OO,HF,FCI,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCINO,SCIOO,SCIPT2NO,SCIPT2OO,SCIrPT2NO,SCIrPT2OO,
start=9,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
FCI=ToExpression[Mol<>"FCI"];
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},
{Thick,Red},{Thick,Blue},
{Thick,Red,Dotted},{Thick,Blue,Dotted}
}
};
FCI={{0.01,FCI},{(10^9),FCI}};
SCINO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIOO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,3]]-HF)},{k,start,Length[NO]}];
SCIPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,3]]-HF)},{k,start,Length[OO]}];
SCIrPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,5]]-HF)},{k,start,Length[NO]}];
SCIrPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,5]]-HF)},{k,start,Length[OO]}];
plot=ListLogLinearPlot[{FCI,SCINO,SCIOO,SCIrPT2NO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{Number of determinants}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{FCI}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}+E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}+E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotRange->{{(10^3),1 (10^8)},Range},PlotOptions];
If[ExpFig,Export[ToString[Mol]<>"_EvsNdet.pdf",plot]];
Return[plot];
];

EvsNdetLO[Mol_,Range_,ExpFig_]:=Module[
{NO,LO,OO,HF,FCI,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCINO,SCILO,SCIOO,SCIPT2NO,SCIPT2LO,SCIPT2OO,SCIrPT2NO,SCIrPT2LO,SCIrPT2OO,
start=9,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
LO=Import[ToLowerCase[Mol]<>"_loc.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
FCI=ToExpression[Mol<>"FCI"];
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},
{Thick,Red},{Thick,Green},{Thick,Blue},
{Thick,Red,Dotted},{Thick,Green,Dotted},{Thick,Blue,Dotted}
}
};
FCI={{0.01,FCI},{(10^9),FCI}};
SCINO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCILO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIOO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,3]]-HF)},{k,start,Length[NO]}];
SCIPT2LO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]+LO[[k,3]]-HF)},{k,start,Length[LO]}];
SCIPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,3]]-HF)},{k,start,Length[OO]}];
SCIrPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,5]]-HF)},{k,start,Length[NO]}];
SCIrPT2LO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]+LO[[k,5]]-HF)},{k,start,Length[LO]}];
SCIrPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,5]]-HF)},{k,start,Length[OO]}];
plot=ListLogLinearPlot[{FCI,SCINO,SCILO,SCIOO,SCIrPT2NO,SCIrPT2LO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{Number of determinants}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{FCI}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{LO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}+E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{LO}+E_\\text{PT2}^\\text{LO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}+E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],Right],
PlotRange->{{(10^3),1 (10^8)},Range},PlotOptions];
If[ExpFig,Export[ToString[Mol]<>"_EvsNdetLO.pdf",plot]];
Return[plot];
];

(Subscript[E, var]) vs (Subscript[E, PT2])

EvsPT2[Mol_,Range_,ExpFig_]:=Module[
{NO,OO,HF,FCI,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCIPT2NO,SCIrPT2NO,SCIPT2OO,SCIrPT2OO,fitPT2NO,fitrPT2NO,fitPT2OO,fitrPT2OO,
start=9,nfit=5,wPT2NO,wrPT2NO,wPT2OO,wrPT2OO,TabPT2,TabrPT2,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
FCI=ToExpression[Mol<>"FCI"];
PlotOptions={Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},{Thick,Red},{Thick,Blue}
}
};
FCI={{-1000,FCI},{100,FCI}};
SCIPT2NO=Table[{(10^3)(NO[[k,3]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIrPT2NO=Table[{(10^3)(NO[[k,5]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIPT2OO=Table[{(10^3)(OO[[k,3]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIrPT2OO=Table[{(10^3)(OO[[k,5]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
wPT2NO=Table[(10^3)NO[[k,4]],{k,start,Length[NO]}];
wrPT2NO=Table[(10^3)NO[[k,6]],{k,start,Length[NO]}];
wPT2OO=Table[(10^3)OO[[k,4]],{k,start,Length[OO]}];
wrPT2OO=Table[(10^3)OO[[k,6]],{k,start,Length[OO]}];
fitPT2NO=Fit[Take[SCIPT2NO,-nfit],{1,x},x];
fitrPT2NO=Fit[Take[SCIrPT2NO,-nfit],{1,x},x];
fitPT2OO=Fit[Take[SCIPT2OO,-nfit],{1,x},x];
fitrPT2OO=Fit[Take[SCIrPT2OO,-nfit],{1,x},x];
plot=Show[{
ListPlot[{FCI,SCIrPT2NO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{$E_\\text{PT2}$ ($mE_h$)}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{FCI}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$ vs $E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$ vs $E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotOptions,PlotRange->{{-200,0},Range}]
,
Plot[{fitrPT2NO,fitrPT2OO},{x,-200,10},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{"<>ToString[nfit]<>"-point linear fit}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotStyle->{{Thick,Dashed,Black},{Thick,Dashed,Black}}]
}];
TabPT2=TableForm[Table[{k,LinearModelFit[Take[SCIPT2OO,-k],{1,x},x,Weights->1/((Take[wPT2OO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
TabrPT2=TableForm[Table[{k,LinearModelFit[Take[SCIrPT2OO,-k],{1,x},x,Weights->1/((Take[wrPT2OO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
Print[TableForm[Table[{k,LinearModelFit[Take[SCIrPT2NO,-k],{1,x},x,Weights->1/((Take[wrPT2NO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}]];
If[ExpFig,Export[ToString[Mol]<>"_EvsPT2.pdf",plot]];
Return[Row[{plot,TabrPT2}]];
];

EvsPT2LO[Mol_,Range_,ExpFig_]:=Module[
{NO,LO,OO,HF,FCI,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCIPT2NO,SCIrPT2NO,SCIPT2LO,SCIrPT2LO,SCIPT2OO,SCIrPT2OO,fitPT2NO,fitrPT2NO,fitPT2OO,fitrPT2OO,
start=9,nfit=4,wPT2NO,wrPT2NO,wPT2LO,wrPT2LO,wPT2OO,wrPT2OO,TabrPT2NO,TabrPT2LO,TabrPT2OO,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
LO=Import[ToLowerCase[Mol]<>"_loc.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
FCI=ToExpression[Mol<>"FCI"];
PlotOptions={Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},{Thick,Red},{Thick,Green},{Thick,Blue}
}
};
FCI={{-1000,FCI},{100,FCI}};
SCIPT2NO=Table[{(10^3)(NO[[k,3]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIrPT2NO=Table[{(10^3)(NO[[k,5]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIPT2LO=Table[{(10^3)(LO[[k,3]]),(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIrPT2LO=Table[{(10^3)(LO[[k,5]]),(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIPT2OO=Table[{(10^3)(OO[[k,3]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIrPT2OO=Table[{(10^3)(OO[[k,5]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
wPT2NO=Table[(10^3)NO[[k,4]],{k,start,Length[NO]}];
wrPT2NO=Table[(10^3)NO[[k,6]],{k,start,Length[NO]}];
wPT2LO=Table[(10^3)LO[[k,4]],{k,start,Length[LO]}];
wrPT2LO=Table[(10^3)LO[[k,6]],{k,start,Length[LO]}];
wPT2OO=Table[(10^3)OO[[k,4]],{k,start,Length[OO]}];
wrPT2OO=Table[(10^3)OO[[k,6]],{k,start,Length[OO]}];
fitPT2NO=Fit[Take[SCIPT2NO,-nfit],{1,x},x];
fitrPT2NO=Fit[Take[SCIrPT2NO,-nfit],{1,x},x];
fitPT2OO=Fit[Take[SCIPT2OO,-nfit],{1,x},x];
fitrPT2OO=Fit[Take[SCIrPT2OO,-nfit],{1,x},x];
plot=Show[{
ListPlot[{FCI,SCIrPT2NO,SCIrPT2LO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{$E_\\text{PT2}$ ($mE_h$)}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{FCI}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$ vs $E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{LO}$ vs $E_\\text{PT2}^\\text{LO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$ vs $E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotOptions,PlotRange->{{-200,10},Range}]
,
Plot[{fitrPT2NO,fitrPT2OO},{x,-200,0},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{"<>ToString[nfit]<>"-point linear fit}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotStyle->{{Thick,Dashed,Black},{Thick,Dashed,Black}}]
}];
TabrPT2NO=TableForm[Table[{k,LinearModelFit[Take[SCIrPT2NO,-k],{1,x},x,Weights->1/((Take[wrPT2NO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
TabrPT2LO=TableForm[Table[{k,LinearModelFit[Take[SCIrPT2LO,-k],{1,x},x,Weights->1/((Take[wrPT2LO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
TabrPT2OO=TableForm[Table[{k,LinearModelFit[Take[SCIrPT2OO,-k],{1,x},x,Weights->1/((Take[wrPT2OO,-k])^2)]["ParameterTable"]},{k,3,7}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
If[ExpFig,Export[ToString[Mol]<>"_EvsPT2LO.pdf",plot]];
Return[Row[{plot,TabrPT2NO,TabrPT2LO,TabrPT2OO}]];
];

MP & CC

MPCC[Mol_,ExpFig_]:=Module[
{SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
MP,CCn,CC,FCI,plot},

MP=ToExpression[Mol<>"MP"];
CCn=ToExpression[Mol<>"CCn"];
CC=ToExpression[Mol<>"CC"];
FCI={{5,ToExpression[Mol<>"FCI"]},{10,ToExpression[Mol<>"FCI"]}};
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->500,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{{"OpenMarkers",Large},{"OpenMarkers",Large},{"OpenMarkers",Large},None},
PlotStyle->{
{Thickness[0.01],Blue},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thick,Black}
}
};
plot=ListPlot[{MP,CCn,CC,FCI},Joined->True,PlotOptions,
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP2, MP3, MP4 \\& MP5}",FontSize->SizeLegend],MaTeX["\\text{CC2, CC3 \\& CC4}",FontSize->SizeLegend],
MaTeX["\\text{CCSD, CCSDT \\& CCSDTQ}",FontSize->SizeLegend],MaTeX["\\text{FCI}",FontSize->SizeLegend]
}],{Right,Top}]];

If[ExpFig,Export[ToString[Mol]<>"_MPCC.pdf",plot]];
Return[plot];
];

Cyclopentadiene

MP & CC calculations

CyclopentadieneHF=-192.808319784581;
CyclopentadieneRCC=1000{-0.7362045408,-0.7355705652,-0.7295372174,-0.7290352049,-0.7274398611,-0.7269614343,-0.7360372650,-0.7287960963,-0.7287762531,-0.7290408720,-0.7289897447,-0.7290409503,-0.7290157099,-0.7318864761,-0.7356278178};
CyclopentadieneFCI=−739.2;
CyclopentadieneMP={{5,-663.374798421},{6,-701.038770308868},{7,-734.485164342225},{8,-733.4333154}};
CyclopentadieneCCn={{5,-669.867722683},{7,-736.574222273275},{9,-738.366684546823}};
CyclopentadieneCC={{6,-707.237579224683},{8,-736.246708418799},{10,-738.202355812839}};

Shanks

s=CyclopentadieneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=CyclopentadieneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=CyclopentadieneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Cyclopentadiene",True]
EvsNdet["Cyclopentadiene",{-760,-300},True]
EvsPT2["Cyclopentadiene",{-760,-400},True]

Furan

MP & CC calculations

FuranHF=-228.643312572484575;
FuranRCC=1000{-0.7652979707,-0.7640344803,-0.7586402265,-0.7576282485,-0.7562814496,-0.7553792406,-0.7644801815,-0.7574181502,-0.7574152071,-0.7579586102,-0.7578481889,-0.7580395522,-0.7579523069,-0.7603286403,-0.7641837740};
FuranFCI=-768.2;
FuranMP={{5,-707.450373824},{6,-727.820193088592},{7,-766.627890777360},{8,-759.8932275}};
FuranCCn={{5,-717.183336927},{7,-765.730048755297},{9,-766.866256888079}};
FuranCC={{6,-734.972685409664},{8,-764.332120385917},{10,-766.65420877679}};

Shanks

s=FuranMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=FuranCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=FuranCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Furan",True]
EvsNdet["Furan",{-780,-300},True]
EvsPT2["Furan",{-780,-450},True]

Imidazole

MP & CC calculations

ImidazoleHF=-224.835356714467;
ImidazoleRCC=1000{-0.7754711401,-0.7745226269,-0.7686145124,-0.7678511205,-0.7661170944,-0.7654219414,-0.7750708607,-0.7676746706,-0.7676857314,-0.7681512324,-0.7680171993,-0.7681505061,-0.7680444720,-0.7704598738,-0.7744687040};
ImidazoleFCI=-778.2;
ImidazoleMP={{5,-720.429915262},{6,-737.828542914060},{7,-777.223689935675},{8,-770.7756855}};
ImidazoleCCn={{5,-729.015795304},{7,-776.111512572204},{9,-777.204281879068}};
ImidazoleCC={{6,-744.198886306645},{8,-774.551173949665},{10,-776.949476371663}};

Shanks

s=ImidazoleMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ImidazoleCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ImidazoleCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Imidazole",True]
EvsNdet["Imidazole",{-810,-300},True]
EvsPT2["Imidazole",{-810,-450},True]

Pyrrole

MP & CC calculations

PyrroleHF=-208.828614693633;
PyrroleRCC=1000{-0.7556655107,-0.7549399199,-0.7490495283,-0.7484673625,-0.7467196077,-0.7461817782,-0.7554301744,-0.7482580045,-0.7482624835,-0.7486191326,-0.7485146561,-0.7486132582,-0.7485346667,-0.7510655180,-0.7549240708};
PyrroleFCI=-758.5;
PyrroleMP={{5,-695.721950709},{6,-720.603108743368},{7,-756.459033548742},{8,-752.2589064}};
PyrroleCCn={{5,-702.531904930},{7,-756.270764152895},{9,-757.576382167585}};
PyrroleCC={{6,-725.712852643528},{8,-755.183721462796},{10,-757.360899120397}};

Shanks

s=PyrroleMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrroleCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrroleCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Pyrrole",True]
EvsNdet["Pyrrole",{-790,-300},True]
EvsPT2["Pyrrole",{-790,-450},True]

Thiophene

MP & CC calculations

ThiopheneHF=-551.321002444800;
ThiopheneRCC=1000{-0.7256446632,-0.7248098582,-0.7183204770,-0.7176578274,-0.7159085879,-0.7152965307,-0.7252235587,-0.7172904562,-0.7173007158,-0.7176747277,-0.7175725190,-0.7177297719,-0.7176561063,-0.7206459265,-0.7248596119};
ThiopheneFCI=-728.9;
ThiopheneMP={{5,-661.487676839},{6,-689.433481554693},{7,-726.576354093504},{8,-721.5988552}};
ThiopheneCCn={{5,-669.535846587},{7,-726.268305928940},{9,-727.662544525096}};
ThiopheneCC={{6,-694.455334004781},{8,-725.135024376793},{10,-727.450489687365}};

Shanks

s=ThiopheneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ThiopheneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ThiopheneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Thiophene",True]
EvsNdet["Thiophene",{-760,-300},True]
EvsPT2["Thiophene",{-760,-400},True]

Benzene

MP & CC calculations

BenzeneHF=-230.722244985640;
BenzeneRCC=1000{-0.8582248386,-0.8575289386,-0.8489396858,-0.8484007771,-0.8462214183,-0.8457060638,-0.8577777063,-0.8476329854,-0.8476271670,-0.8479946246,-0.8478518864,-0.8480063720,-0.8478950189,-0.8526084534,-0.8569337423};
BenzeneFCI=-862.9;
BenzeneMP={{5,-782.332077228},{6,-816.387142630248},{7,-858.539911321773},{8,-853.7830144}};
BenzeneCCn={{5,-789.412298096},{7,-859.142698599615},{9,-860.586074871286}};
BenzeneCC={{6,-821.788776613854},{8,-857.926313401076},{10,-860.365191225800}};

Shanks

s=BenzeneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=BenzeneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=BenzeneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Benzene",True]
EvsNdet["Benzene",{-890,-300},True]
EvsPT2["Benzene",{-890,-550},True]

EvsNdetLO["Benzene",{-890,-300},True]

Pyrazine

MP & CC calculations

PyrazineHF=-262.703010944756;
PyrazineRCC=1000{-0.9004303611,-0.8994208348,-0.8904760506,-0.8896927223,-0.8874173342,-0.8866805026,-0.8998443413,-0.8889931526,-0.8890056278,-0.8895707081,-0.8893595365,-0.8895819294,-0.8894088709,-0.8939949868,-0.8987118525};
PyrazineFCI=-904.6;
PyrazineMP={{5,-834.617733280},{6,-853.655354014131},{7,-902.907089183363},{8,-893.8350552}};
PyrazineCCn={{5,-844.463447870},{7,-901.497912273981},{9,-902.636842327822}};
PyrazineCC={{6,-861.028517352127},{8,-899.350733684886},{10,-902.330775312939}};

Shanks

s=PyrazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Pyrazine",True]
EvsNdet["Pyrazine",{-930,-300},True]
EvsPT2["Pyrazine",{-930,-600},True]

Pyridazine

MP & CC calculations

PyridazineHF=-262.669873445804;
PyridazineRCC=1000{-0.9051346468,-0.9040950620,-0.8948571481,-0.8940526661,-0.8917314365,-0.8909739205,-0.9045811436,-0.8933621901,-0.8933692724,-0.8939578832,-0.8937286400,-0.8939693617,-0.8937813845,-0.8984963810,-0.9032998712};
PyridazineFCI=-908.8;
PyridazineMP={{5,-838.740583969},{6,-857.275882097803},{7,-907.925790862876},{8,-898.2587542}};
PyridazineCCn={{5,-848.908853611},{7,-906.214393900430},{9,-907.453759605642}};
PyridazineCC={{6,-864.874528282081},{8,-903.988565095408},{10,-907.116636262810}};

Shanks

s=PyridazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Pyridazine",True]
EvsNdet["Pyridazine",{-930,-300},True]
EvsPT2["Pyridazine",{-930,-600},True]

Pyridine

MP & CC calculations

PyridineHF=-246.715184707013;
PyridineRCC=1000{-0.8786610490,-0.8777322873,-0.8690248653,-0.8683017127,-0.8661232011,-0.8654495310,-0.8780294149,-0.8675431229,-0.8675498034,-0.8680195252,-0.8678492510,-0.8680324990,-0.8678951412,-0.8725611799,-0.8770579247};
PyridineFCI=-882.7;
PyridineMP={{5,-807.471827567},{6,-834.035340573813},{7,-879.923597854822},{8,-872.875093}};
PyridineCCn={{5,-816.328319360},{7,-879.599675234389},{9,-880.821972634781}};
PyridineCC={{6,-840.701382579433},{8,-877.874903251700},{10,-880.821972634781}};

Shanks

s=PyridineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Pyridine",True]
EvsNdet["Pyridine",{-930,-300},True]
EvsPT2["Pyridine",{-930,-550},True]

Pyrimidine

MP & CC calculations

PyrimidineHF=-262.713652796899;
PyrimidineRCC=1000{-0.8974977037,-0.8962253597,-0.8874909761,-0.8864916123,-0.8843882053,-0.8834862040,-0.8965079019,-0.8857025445,-0.8857277305,-0.8862904860,-0.8861077546,-0.8863063548,-0.8861548350,-0.8907977274,-0.8954882322};
PyrimidineFCI=-900.5;
PyrimidineMP={{5,-830.057493278},{6,-849.612212994749},{7,-899.266633591386},{8,-889.9912031}};
PyrimidineCCn={{5,-841.308837134},{7,-898.365293520950},{9,-899.263868742531}};
PyrimidineCC={{6,-857.976308572695},{8,-896.080430191809},{10,-898.976078520330}};

Shanks

s=PyrimidineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrimidineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrimidineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Pyrimidine",True]
EvsNdet["Pyrimidine",{-930,-300},True]
EvsPT2["Pyrimidine",{-930,-600},True]

Tetrazine

MP & CC calculations

TetrazineHF=-294.615743073901;
TetrazineRCC=1000{-0.9535699581,-0.9522481897,-0.9421491360,-0.9411276503,-0.9385791089,-0.9376153043,-0.9529477782,-0.9404679331,-0.9404954968,-0.9412752232,-0.9409591463,-0.9412780709,-0.9410139720,-0.9458312403,-0.9513041455};
TetrazineFCI=-957.9;
TetrazineMP={{5,-895.922989130},{6,-899.456957539510},{7,-958.570330486010},{8,-944.2694261}};
TetrazineCCn={{5,-908.969490669},{7,-954.853218744419},{9,-955.880388848436}};
TetrazineCC={{6,-909.100948888639},{8,-951.585113405389},{10,-955.428165912650}};

Shanks

s=TetrazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TetrazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TetrazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Tetrazine",True]
EvsNdet["Tetrazine",{-990,-300},True]
EvsPT2["Tetrazine",{-990,-650},True]

Triazine

MP & CC calculations

TriazineHF=-278.717319389695;
TriazineRCC=1000{-0.9148109404,-0.9131440209,-0.9044723623,-0.9031539125,-0.9133607546,-0.9011758455,-0.9000120112,-0.9023070600,-0.9023519040,-0.9029977074,-0.9028144404,-0.9030248015,-0.9028686620,-0.9074925601,-0.9124679305};
TriazineFCI=-918.4;
TriazineMP={{5,-850.519282476},{6,-863.593139716035},{7,-916.717801063422},{8,-905.4360103}};
TriazineCCn={{5,-864.406418639},{7,-915.583810723581},{9,-916.075626870853}};
TriazineCC={{6,-873.819918012385},{8,-912.716493155011},{10,-915.770573661020}};

Shanks

s=TriazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TriazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TriazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

MPCC["Triazine",True]
EvsNdet["Triazine",{-940,-300},True]
EvsPT2["Triazine",{-940,-600},True]

Statistics

FCI=
{CyclopentadieneFCI,FuranFCI,ImidazoleFCI,PyrroleFCI,ThiopheneFCI,
BenzeneFCI,PyrazineFCI,PyridazineFCI,PyridineFCI,PyrimidineFCI,TetrazineFCI,TriazineFCI};

MP=Table[
{CyclopentadieneMP[[k,2]],FuranMP[[k,2]],ImidazoleMP[[k,2]],PyrroleMP[[k,2]],ThiopheneMP[[k,2]],
BenzeneMP[[k,2]],PyrazineMP[[k,2]],PyridazineMP[[k,2]],PyridineMP[[k,2]],PyrimidineMP[[k,2]],TetrazineMP[[k,2]],TriazineMP[[k,2]]}
,{k,Length[CyclopentadieneMP]}];

CCn=Table[
{CyclopentadieneCCn[[k,2]],FuranCCn[[k,2]],ImidazoleCCn[[k,2]],PyrroleCCn[[k,2]],ThiopheneCCn[[k,2]],
BenzeneCCn[[k,2]],PyrazineCCn[[k,2]],PyridazineCCn[[k,2]],PyridineCCn[[k,2]],PyrimidineCCn[[k,2]],TetrazineCCn[[k,2]],TriazineCCn[[k,2]]}
,{k,Length[CyclopentadieneCCn]}];

CC=Table[
{CyclopentadieneCC[[k,2]],FuranCC[[k,2]],ImidazoleCC[[k,2]],PyrroleCC[[k,2]],ThiopheneCC[[k,2]],
BenzeneCC[[k,2]],PyrazineCC[[k,2]],PyridazineCC[[k,2]],PyridineCC[[k,2]],PyrimidineCC[[k,2]],TetrazineCC[[k,2]],TriazineCC[[k,2]]}
,{k,Length[CyclopentadieneCC]}];

RCC=Table[
{CyclopentadieneRCC[[k]],FuranRCC[[k]],ImidazoleRCC[[k]],PyrroleRCC[[k]],ThiopheneRCC[[k]],
BenzeneRCC[[k]],PyrazineRCC[[k]],PyridazineRCC[[k]],PyridineRCC[[k]],PyrimidineRCC[[k]],TetrazineRCC[[k]],TriazineRCC[[k]]}
,{k,Length[CyclopentadieneRCC]}];

TableForm[
Table[SetAccuracy[{Mean[Abs[MP[[n]]-FCI]],Mean[MP[[n]]-FCI],Max[Abs[MP[[n]]-FCI]],Min[Abs[MP[[n]]-FCI]]},2],{n,Length[MP]}],
TableHeadings->{{"MP2","MP3","MP4","MP5"},{"MAE","MSE","Max","Min"}}]
TableForm[
Table[SetAccuracy[{Mean[Abs[CCn[[n]]-FCI]],Mean[CCn[[n]]-FCI],Max[Abs[CCn[[n]]-FCI]],Min[Abs[CCn[[n]]-FCI]]},2],{n,Length[CCn]}],TableHeadings->{{"CC2","CC3","CC4"},{"MAE","MSE","Max","Min"}}]
TableForm[
Table[SetAccuracy[{Mean[Abs[CC[[n]]-FCI]],Mean[CC[[n]]-FCI],Max[Abs[CC[[n]]-FCI]],Min[Abs[CC[[n]]-FCI]]},2],{n,Length[CC]}],TableHeadings->{{"CCSD","CCSDT","CCSDTQ"},{"MAE","MSE","Max","Min"}}]
TableForm[
Table[SetAccuracy[{Mean[Abs[RCC[[n]]-FCI]],Mean[RCC[[n]]-FCI],Max[Abs[RCC[[n]]-FCI]],Min[Abs[RCC[[n]]-FCI]]},2],{n,Length[RCC]}],TableHeadings->{{"CCSD[T]","CCSD(T)","R-CCSD[T]","R-CCSD(T)","CCSD(TQ),B","CR-CCSD[T]","CR-CCSD(T)","R1-CCSD(TQ),A","R1-CCSD(TQ),B","R2-CCSD(TQ),A","R2-CCSD(TQ),B","CR-CCSD(TQ),A","CR-CCSD(TQ),B","CR-CC(2,3),A","CR-CC(2,3)"},{"MAE","MSE","Max","Min"}}]